Refractive Index - Lens question

AI Thread Summary
A double concave lens with equal radii of curvature of 15.1 cm forms a virtual image 5.0 cm from the lens when an object is placed 14.2 cm away. The calculations for the focal length yield a value of 1/f = 0.27, but the focal length is negative due to the sign convention for virtual images. Using the lens maker's equation, the refractive index calculation initially resulted in an incorrect value of 3.03, prompting a reevaluation of the sign convention. After applying the correct sign convention, the refractive index was recalculated to be approximately 1.98, which aligns with one of the answer choices. The discussion emphasizes the importance of sign conventions in lens calculations.
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Homework Statement



A double concave lens has equal radii of curvature of 15.1 cm. An object placed 14.2 cm from the lens forms a virtual image 5.0 cm from the lens. What is the index of refraction of the lens material?

A. 1.98
B. 1.9
C. 1.84
D. 2.06

Homework Equations



1/f = (n – 1 ) (1/R1 - 1/R2 )
1/f = 1/do + 1/di

The Attempt at a Solution



1/f = 1/14.2 + 1/5.0 so i get 1/f = 0.27

1/f = (n – 1 ) (1/R1 - 1/R2 )
0.27 = (n-1) (1/15.1 - (-1/15.1)

this results in an n equal to about 3.03 which is not close to any of the answers, though I'm sure i have the right equations, I'm just not sure what I'm doing wrong?
are these only applicable to convex lens?
 
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I am getting n=1.98 .Is this the correct answer ?
 
Vibhor said:
I am getting n=1.98 .Is this the correct answer ?

i'm not sure if that is right but it is an answer choice. what method did you use?
 
The problem is with the calculation of focal length . You should be very careful with whatever sign convention you are using . 1/f is coming out to be -0.13 cm . I am using new coordinate sign convention where the direction of incident rays is considered positive .In this sign convention both the object as well as image distance is negative.
 
If the image is virtual than di is negative (according with the most common sign convention which seems to be the one used here).
 
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